Least Common Multiple (LCM) of 157 and 54
The least common multiple (LCM) of 157 and 54 is 8478.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 157 and 54?
First, calculate the GCD of 157 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 54 = 2 remainder 49 |
| 2 | 54 ÷ 49 = 1 remainder 5 |
| 3 | 49 ÷ 5 = 9 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 18 | 1224 |
| 40 and 59 | 2360 |
| 117 and 91 | 819 |
| 12 and 109 | 1308 |
| 133 and 192 | 25536 |